Lobachevsky …

• Nikolai Ivanovich Lobachevsky was a Russian (1792 - 1856).
• He received a physics and mathematics degree from a friend and teacher of Gauss.
• He developed a new geometry very much like Bolyai's ideas - yet uncovered completely on his own.
• He called it Hyperbolic Geometry. It was a non-Euclidean Geometry which was built on curved surfaces rather than flat ones.
• Lobachevsky and Bolyai were first to try to prove Euclid's 5th Postulate (the famous 'Parallel Postulate'); but they felt it was impossible.
• Gauss, Boyai, and Lobachevsky were unaware of each other's work.
• He was the first to publish the idea of non-Euclidean Geometry. He published several times for a number of years in several languages. No one noticed because the world could not understand that these ideas were important. Finally the Tsar awarded him a diamond ring. He was credited as a discoverer of non-Euclidean Geometry.
• Lobachevsky, Gauss, and Bolyai saw a geometry where there are more than 1 parallel line through a point outside a given line. This describes a plane that is curved negatively, like the inside of a balloon. It is called an Elliptic geometry.